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PLoS ONE

An optimized initialization for LDPC decoding over GF(q) in impulsive noise environments

Haoqiang Liu, Hongbo Zhao, Xiaowen Chen, Wenquan Feng

Published May 6, 2021• 1 citation
Publisher

Abstract

Modern navigation satellite communication has the characteristic of high transmitting rate. To avoid bit errors in data transmission, low density parity check (LDPC) codes are widely recognized as efficient ways for navigation communication. Conventionally, the LDPC decoding is applied for additive white Gaussian noise (AWGN) channel and degrades severely while facing the impulsive noise. However, navigation communication often suffers from impulsive interference due to the occurrence of high amplitude "spikes". At this time, the conventional Gaussian noise assumption is inadequate. The impulsive component of interference has been found to be significant which influences the reliability of transmitted information. Therefore the LDPC decoding algorithms for AWGN channel are not suitable for impulsive noise environments. Consider that LDPC codes over GF(q) perform better than binary LDPC in resisting burst errors for current navigation system, it is necessary to conduct research on LDPC codes over GF(q). In this paper, an optimized initialization by calculating posterior probabilities of received symbols is proposed for non-binary LDPC decoding on additive white Class A noise (AWAN) channel. To verify the performance of the proposed initialization, extensive experiments are performed in terms of convergence, validity, and robustness. Preliminary results demonstrate that the decoding algorithm with the optimized initialization for non-binary LDPC codes performs better than the competing methods and that of binary LDPC codes on AWAN channel.

DOI
10.1371/journal.pone.0250930

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Modern navigation satellite communication has the characteristic of high transmitting rate. To avoid bit errors in data transmission, low density parity check (LDPC) codes are widely recognized as efficient ways for navigation communication. Conventionally, the LDPC decoding is applied for additive white Gaussian noise (AWGN) channel and degrades severely while facing the impulsive noise. However, navigation communication often suffers from impulsive interference due to the occurrence of high amplitude "spikes". At this time, the conventional Gaussian noise assumption is inadequate. The impulsive component of interference has been found to be significant which influences the reliability of transmitted information. Therefore the LDPC decoding algorithms for AWGN channel are not suitable for impulsive noise environments. Consider that LDPC codes over GF(q) perform better than binary LDPC in resisting burst errors for current navigation system, it is necessary to conduct research on LDPC codes over GF(q). In this paper, an optimized initialization by calculating posterior probabilities of received symbols is proposed for non-binary LDPC decoding on additive white Class A noise (AWAN) channel. To verify the performance of the proposed initialization, extensive experiments are performed in terms of convergence, validity, and robustness. Preliminary results demonstrate that the decoding algorithm with the optimized initialization for non-binary LDPC codes performs better than the competing methods and that of binary LDPC codes on AWAN channel.
Communications systems suffer from impulsive in- terference, generally modeled as a memory channel to account for the inherent bursts of impulse even though conventional receivers take into account the additive white Gaussian noise only. In this paper, finite- field based constructions of Low Density Parity Check (LDPC) coding over the Markov Gaussian channel are investigated. In contrast with existing approaches assuming the impulse noise statistics, this paper proposes a modified maximum- a-priori method, which forfeits using the statistical knowledge of impulse, to estimate whether or not each transmitted symbol is corrupted by impulse noise. Subsequently, the sum-product algorithm LDPC decoder invokes a clipper to diminish impulsive interference when the channel state is identified to be impulse- corrupted. The bit error rate (BER) performance versus the signal-to-noise ratio for the proposed decoder is conducted using computer simulation. The experimental results in terms of the BER performance justified the robustness of our proposed receiver and also revealed its competitiveness with the optimal benchmark decoder in the hostile environment. Moreover, using the proposed receiver, our calibrated quasi-cyclic LDPC code is shown to slightly outperform its 5G New Radio counterpart under certain circumstances.
In some practical applications, impulsive noise can severely degrade the performance of a communication system. As a class of powerful error correction codes, Low-density parity-check (LDPC) codes ha,ve been shown superior performance on AWGN channels. In addition, belief propagation (BP) decoding algorithm of LDPC codes based on scheduling strategy has better performance and faster convergence rate than conventional BP decoding algorithm. In this paper, a dynamic scheduling of LDPC codes is first used on impulsive noise channels. Moreover, we propose a new scheduling strategy which named grouping dynamic scheduling (GDS) for impulsive noise channels to further improve the performance. Simulation results show that the dynamic scheduling on impulsive noise channels provides more performance gain than AWGN channels and the gain becomes significant when the channel is more impulsive. In addition, compared with conventional dynamic scheduling strategy, our proposed algorithm not only provides better performance, but also lowers the actual decoding computational complexity.
In this paper, a transmission scheme based on Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes with an invertible quasi-cyclic Matrix Q is proposed over Additive White Gaussian Noise (AWGN) channel in order to obtain faster convergence of hard-decision decoding. Combined with the soft information from channel, another improved Reliability-based Q (RQ) decoding algorithm is proposed. The new design can also be applied to QC-LDPC codes in IEEE 802.16e Standards. The simulation results show that the proposed scheme with Q or RQ decoding algorithm has better error correction performance and lower average number of iterations than Bit-Flipping (BF) or weighted Bit-Flipping (WBF) decoding algorith
This paper extends the work on density evolution for binary low-density parity-check (LDPC) codes with Gaussian approximation to LDPC codes over GF(q) . We first generalize the definition of channel symmetry for nonbinary inputs to include q-ary phase-shift keying (PSK) modulated channels for prime q and binary-modulated channels for q that is a power of 2. For the well-defined q-ary-input symmetric-output channel, we prove that under the Gaussian assumption, the density distribution for messages undergoing decoding is fully characterized by (q-1) quantities. Assuming uniform edge weights, we further show that the density of messages computed by the check node decoder (CND) is fully defined by a single number. We then present the approximate density evolution for regular and irregular LDPC codes, and show that the (q-1) -dimensional integration involved can be simplified using a dimensionality reduction algorithm for the important case of q=2p. Through application of approximate density evolution and linear programming, we optimize the degree distribution of LDPC codes over GF(3) and GF(4). The optimized irregular LDPC codes demonstrate performance close to the Shannon capacity for long codewords. We also design GF(q) codes for high-order modulation by using the idea of a channel adapter. We find that codes designed in this fashion outperform those optimized specifically for the binary additive white Gaussian noise (AWGN) channel for a short codewords and a spectral efficiency of 2 bits per channel use (b/cu).
Low-density parity-check (LDPC) codes with very long block lengths are well known for their powerful error correction, but it is not always desirable to employ long codes in communication systems, where latency is a serious issue, such as voice and video communication between multiple users. Finite length analyses of LDPC codes have already been presented in the literature for the additive white Gaussian noise channel, but in this paper, we consider the finite length analysis of LDPC codes for channels that exhibit impulsive noise. First, an exact uncoded bit error probability (BEP) of an impulsive noise channel, modeled as a symmetric α-stable (SαS) distribution, is derived. Then, to obtain the LDPC-coded performance, density evolution is applied to evaluate the asymptotic performance of LDPC codes on SαS channels and determine the threshold signal-to-noise ratio. Finally, we derive closed-form expressions for the BEP and block error probability of short LDPC codes on these channels, which are shown to match closely with simulated results on channels with different levels of impulsiveness, even for block lengths as low as 1000 b.
Designing realizable Maximum Likelihood (ML) decoders for low-density parity-check (LDPC) codes has always been a challenging problem. Maxwell decoder is a well-known ML decoder for LDPC codes over a binary erasure channel (BEC). Based on the concept used in the Maxwell decoder, it may be possible to design near-ML decoders for LDPC codes over an additive white Gaussian noise (AWGN) channel. In this paper, we introduce a novel idea called channel transformation, which will be used as a bridge linking a BEC channel and an AWGN channel. With the transformation, we further propose a near-ML decoder for LDPC codes sent over an AWGN channel. The proposed near-ML decoder, combining a Belief Propagation (BP) decoder and a Maxwell decoder, is called the BP-Maxwell (BM) decoder. Simulation results show that compared with a BP decoder, the BM decoding algorithm can accomplish better frame error rates (FERs) by eliminating many of the error frames with a smaller percentage of error bits. Thus, the BM decoder is a step closer to the ML decoder compared with the BP decoder.